>>513002203
This relies on two things
First that GB even wanted to support the CSA. Britain profited from cheap cotton sure but they already had a surplus of cotton from their colonies in Egypt and India. They were the most abolitionist power on earth and would never has risked their own men in a war over the CSA
Second you're assuming European powers could not only arm but also man a war against the union. Even at the outbreak of the war the United States (almost entirely the union states) was the second largest industrial power on earth. Britain could in theory out produce them but in terms of manpower, as I mentioned above, there was no way british men would land in Virginia and fight in this war nor was the empire too keen to arm their colonies (which wouldn't happen until the existential threat of the world wars.)
So you would need other european powers to also ally with Britain and the CSA in order to take down the Union. France was busy in Mexico and Germany was still in the process of uniting under the prussians.
The industrial power you're alluding to simply doesn't exist in the capacity needed to defeat the union. The war was a lost cause from the start there is no way for it to end in victory. The only possible resolution that kept the CSA intact was a union vote against the war and against Lincoln in 63 however by that time the union had already effectively won the war with the blockades and the gettysburg campaign so the public re-elected Lincoln and sealed the confederate fate (Note even if the union voted against the war in 63 the CSA was still doomed to become either a british puppet state, a partner in a strange franco-mexican empire, or simply re-absorbed into the union after they inevitably abolished slavery.